A high-order combined finite element/interpolation approach for multidimensional nonlinear generalized Benjamin–Bona–Mahony–Burgers equation

Eric Ngondiep

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 215, issue C, 560-577

Abstract: A high-order combined finite element/interpolation approach is developed for solving a multidimensional nonlinear generalized Benjamin–Bona–Mahony–Burgers equation subjected to suitable initial and boundary conditions. In the proposed high-order scheme we approximate the time derivative with piecewise polynomial interpolation of second-order and use the finite element discretization of piecewise polynomials of degree q and q+1, where q≥2 is an integer, to approximating the space derivatives. The stability together with the error estimates of the constructed technique are established in W21(Ω)-norm. The analysis suggests that the developed numerical scheme is unconditionally stable, temporal second-order accurate and convergence in space with order q. Furthermore, the new procedure is faster and more efficient than a broad range of numerical methods discussed in the literature for the given initial–boundary value problem. A wide set of examples are performed to confirming the theoretical studies.

Keywords: Multidimensional nonlinear generalized Benjamin–Bona–Mahony–Burgers equations; Piecewise polynomial interpolation; Finite element method; Combined finite element/interpolation approach; Unconditional stability; Error estimates (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:215:y:2024:i:c:p:560-577

DOI: 10.1016/j.matcom.2023.08.041

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